# Unbounded Violation of Tripartite Bell Inequalities

@article{PrezGarca2007UnboundedVO,
title={Unbounded Violation of Tripartite Bell Inequalities},
author={David P{\'e}rez-Garc{\'i}a and Michael M. Wolf and Carlos Palazuelos and Ignacio Villanueva and Marius Junge},
journal={Communications in Mathematical Physics},
year={2007},
volume={279},
pages={455-486}
}
We prove that there are tripartite quantum states (constructed from random unitaries) that can lead to arbitrarily large violations of Bell inequalities for dichotomic observables. As a consequence these states can withstand an arbitrary amount of white noise before they admit a description within a local hidden variable model. This is in sharp contrast with the bipartite case, where all violations are bounded by Grothendieck’s constant. We will discuss the possibility of determining the… Expand

#### Figures from this paper

Efficiency of higher-dimensional Hilbert spaces for the violation of Bell inequalities
• Physics
• 2008
We have determined numerically the maximum quantum violation of over 100 tight bipartite Bell inequalities with two-outcome measurements by each party on systems of up to four dimensional HilbertExpand
Large Violation of Bell Inequalities with Low Entanglement
• Mathematics, Physics
• 2011
In this paper we obtain violations of general bipartite Bell inequalities of order $${\frac{\sqrt{n}}{\log n}}$$ with n inputs, n outputs and n-dimensional Hilbert spaces. Moreover, we constructExpand
On the largest Bell violation attainable by a quantum state
We study the projective tensor norm as a measure of the largest Bell violation of a quantum state. In order to do this, we consider a truncated version of a well-known SDP relaxation for the quantumExpand
Unbounded Violations of Bipartite Bell Inequalities via Operator Space Theory
• Mathematics, Physics
• 2010
In this work we show that bipartite quantum states with local Hilbert space dimension n can violate a Bell inequality by a factor of order $${{\rm \Omega} \left(\frac{\sqrt{n}}{\log^2n} \right)}$$Expand
Near-Optimal and Explicit Bell Inequality Violations
• Mathematics, Computer Science
• Theory Comput.
• 2012
Two new two-player games with Bell inequality violations that are stronger, fully explicit, and arguably simpler than earlier work are given. Expand
Near-Optimal and Explicit Bell Inequality Violations
• 2012
Entangled quantum systems can exhibit correlations that cannot be simulated classically. For historical reasons such correlations are called “Bell inequality violations.” We give two new two-playerExpand
Near-Optimal and Explicit Bell Inequality Violations
• 2012
Entangled quantum systems can exhibit correlations that cannot be simulated classically. For historical reasons such correlations are called “Bell inequality violations.” We give two new two-playerExpand
Quantum bounds on Bell inequalities
• Physics
• 2009
We have determined the maximum quantum violation of 241 tight bipartite Bell inequalities with up to five two-outcome measurement settings per party by constructing the appropriate measurementExpand
Local quasi hidden variable modelling and violations of Bell-type inequalities by a multipartite quantum state
We introduce for a general correlation scenario a new simulation model, a local quasi hidden variable (LqHV) model, where locality and the measure-theoretic construction inherent to a local hiddenExpand
Local hidden?variable models for entangled quantum states
• Mathematics, Physics
• 2014
While entanglement and violation of Bell inequalities were initially thought to be equivalent quantum phenomena, we now have different examples of entangled states whose correlations can be describedExpand

#### References

SHOWING 1-10 OF 91 REFERENCES
Bell inequality with an arbitrary number of settings and its applications
• Physics
• 2006
Based on a geometrical argument introduced by Zukowski, a new multisetting Bell inequality is derived, for the scenario in which many parties make measurements on two-level systems. This generalizesExpand
Aspects of Generic Entanglement
• Mathematics, Physics
• 2006
We study entanglement and other correlation properties of random states in high-dimensional bipartite systems. These correlations are quantified by parameters that are subject to the concentrationExpand
Extremal quantum correlations for N parties with two dichotomic observables per site
Consider a scenario where $N$ separated quantum systems are measured, each with one among two possible dichotomic observables. Assume that the $N$ events corresponding to the choice and performanceExpand
Grothendieck's constant and local models for noisy entangled quantum states
• Physics
• 2006
We relate the nonlocal properties of noisy entangled states to Grothendieck's constant, a mathematical constant appearing in Banach space theory. For two-qubit Werner states rho p WExpand
Multiplicativity of Completely Bounded p-Norms Implies a New Additivity Result
• Mathematics, Physics
• 2006
AbstractWe prove additivity of the minimal conditional entropy associated with a quantum channel Φ, represented by a completely positive (CP), trace-preserving map, when the infimum of S(γ12) − S(γ1)Expand
Bell’s inequalities and distillability in N -quantum-bit systems
• Physics
• 2002
The relation between Bell inequalities with two two-outcome measurements per site and distillability is analyzed in systems of an arbitrary number of quantum bits. We observe that the violation ofExpand
Entanglement versus bell violations and their behavior under local filtering operations.
• Mathematics, Medicine
• Physical review letters
• 2002
The optimal local filtering operations leading to the maximal Bell violation for a given state are provided, and the special role of the resulting Bell diagonal states in the context of Bell inequalities is discussed. Expand
Separable balls around the maximally mixed multipartite quantum states
• Physics
• 2003
We show that for an m-partite quantum system, there is a ball of radius 2{sup -(m/2-1)} in Frobenius norm, centered at the identity matrix, of separable (unentangled) positive semidefinite matrices.Expand
Experimental violation of a Bell's inequality with efficient detection
Here, correlations in the classical properties of massive entangled particles (9Be+ ions): these correlations violate a form of Bell's inequality, and the high detection efficiency of the apparatus eliminates the so-called ‘detection’ loophole. Expand
Experimental violation of a cluster state bell inequality.
• Physics, Medicine
• Physical review letters
• 2005
It is experimentally demonstrate that correlations in a four-qubit linear cluster state cannot be described by local realism, and a cluster-state Bell parameter of 2.59+/-0.08 is observed, which is more than 7sigma larger than the threshold of 2 imposed byLocal realism. Expand